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# Find the locus of a point which moves such that its distance from the origin is three times is distance from x-axis.

Answer :

Key points to solve the problem:

• Idea of distance formula- Distance between two points A(x_{1},y_{1}) and B(x_{2},y_{2}) is given by- AB =

How to approach: To find locus of a point we first assume the coordinate of point to be (h, k) and write a mathematical equation as per the conditions mentioned in question and finally replace (h, k) with (x, y) to get the locus of point.

Let the coordinates of point whose locus is to be determined be (h, k)

As we need to maintain a distance of (h,k) from origin such that it is 3 times the distance from x-axis.

So we select point (h,0) on x-axis.

From distance formula:

Distance of (h,k) from (0,0) =

Distance of (h,k) from (h,0) =

According to question both distance are same.

∴

Squaring both sides:

⇒

Replace (h,k) with (x,y)

Thus, locus of point is …

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